Bivariate Scaling Relationship Between Stochastic Perturbation and Critical Proximity in Nonlinear Dynamical Systems

This document records a mathematical scaling relationship describing how stochastic perturbations interact with proximity to critical transitions in nonlinear dynamical systems. An empirically observed bivariate scaling form is stated, along with a derived perturbation threshold relationship and a hub-dependent geometric correction factor. A validation taxonomy is provided to delineate confirmed empirical baselines from theoretical predictions. This memorandum places the mathematical relationships into the public scientific record to establish definitive prior art and ensure open accessibility. This work is a preprint. The original data record and timestamped version are archived at Zenodo: https://doi.org/10.5281/zenodo.18825703 GitHub repository: https://github.com/devinromberger123-prog/rgl-scalingSoftware DOI: https://doi.org/10.5281/zenodo.19212391 Supplementary Material File (version 7-0.pdf) - Download - 206.87 KB Information & Authors Information Copyright This work is licensed under a Non Exclusive No Reuse License.

Authors Metrics & Citations Metrics Article Usage 148views 53downloads Citations Download citation Devin Romberger. Bivariate Scaling Relationship Between Stochastic Perturbation and Critical Proximity in Nonlinear Dynamical Systems. Authorea. 01 April 2026. DOI: https://doi.org/10.22541/au.177437412.27831305/v2 DOI: https://doi.org/10.22541/au.177437412.27831305/v2 If you have the appropriate software installed, you can download article citation data to the citation manager of your choice. Simply select your manager software from the list below and click Download. For more information or tips please see 'Downloading to a citation manager' in the Help menu.